The present invention relates to devices and methods for error detection and error isolation in redundant physical systems and in particular to devices and methods for determining a physical quantity from a number of measured values containing errors, wherein the physical quantity is defined by a measured quantity or a plurality of measured quantities, and wherein the number of measurements is higher than the number of (unknown) measured quantities.
For the identification of individual errors, a comparison of a so-called parity vector to the characteristic error lines (bias lines or “failure-direction-lines”) is executed for each satellite [3], [4], [5]. With simultaneously occurring multiple errors, in the previous years different algorithms were used. Mainly, they are based on subset checks. One of these algorithms is the RANCO algorithm [11]. RANCO is based on the so-called RANSAC algorithm, which is common in robotics. From a minimum number of measurements, i.e. from a number of measurements which is as small as possible, the same calculates a number of possible solutions in order to generate the model. From each of those solutions, the difference between the actual model and all remaining measurements is calculated. The result is compared to a fixed threshold value. In this form, so-called inliers and outliers are determined. From the set having the greatest number of inliers, the model is newly calculated, i.e. the residual measurements (outliers) are evaluated to be erroneous and ignored. A threshold value to execute this decision is here selected empirically.
Determining a physical quantity from measured values containing errors may, however, not only be executed for the satellite navigation, but in all fields of physics, i.e. for position determination, determining a distance, a pressure, a temperature, a speed, an acceleration, an area, a volume, an electrical quantity, a magnetic quantity, an optical quantity or a hydraulic quantity, as far as measurements are executed in this respect which may be erroneous which will be the case with typical measurements.
With such applications, it is often an objective to estimate physical quantities from the measurements. Apart from this, a linear model exists representing the connection between measurements and physical quantities. Thus, for example, with a regression line, the position of the regression line is to be estimated. Its inclination and/or its Y-Section then represent the requested physical magnitude. The regression line may here be executed by measurements of different points, which all ought to be located on the line, wherein measurement errors may be considerable, wherein the measurement errors are on one hand typical noise and on the other hand, a typical constant error, which is also referred to as offset.
Long since, however, in the field of satellite navigation, the evaluation of redundant measured values containing errors has gained more and more importance. Position determination with satellite navigation systems is based on pseudo-distance measurements (pseudo-range measurements) and phase measurements. These measurements are frequently affected by certain phenomena like reflection and diffraction which may not be detected or corrected during the signal processing steps executed before position determination. Such interferences result in measurement errors also referred to as “bias” associated with the measurements. With the introduction of new global navigation satellite systems like Galileo it may be expected that on average 18 satellites are in the field of view and that a minimum of 13 satellites are in the field of view. This not only leads to a higher redundancy for position determination, but also to more possible error sources. Thus, in particular with such a proceeding, the assumption of one single erroneous signal is no longer valid.
The first objective of so-called error detection and identification technologies (FDI technologies) is the detection, i.e. to determine whether at least one erroneous measurement exists. This is treated as a hypothesis test problem. The null hypothesis (H0) corresponds to the case that no error is present, while the alternative hypothesis (H1) corresponds to the erroneous case. In the past years, some approaches were represented under the headword RAIM, as they are described in [2]. The identification of individual errors is achieved by comparing a parity vector to the characteristic bias-line of each satellite, as it is described in [3], [4] and [5]. The identification of several errors may be executed by testing measurement subgroups as it is described in [1].
It is, in particular, disadvantageous with regard to this conventional technology, that the threshold value has to be determined empirically and that a hard decision has to be executed between erroneous measurement and non-erroneous measurement, i.e. that the “good rest” of an erroneous measurement is also discarded or that when an erroneous measurement is not eliminated, an unnecessitated error is introduced as this measurement is used for determining the physical quantity.